Schwarzschild coordinates

E41074

coordinate system general relativity concept spherical coordinate system

Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.

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All labels observed (3)

Label	Occurrences
Schwarzschild coordinates canonical	8
Schwarzschild radial coordinate	1
Schwarzschild-like coordinates	1

How this entity was disambiguated

This entity first appeared as the object of triple T311431 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Schwarzschild coordinates
Context triple: [Schwarzschild radius, coordinateSingularityAt, Schwarzschild coordinates]

A. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
B. Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
C. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
D. Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
E. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Schwarzschild coordinates
Target entity description: Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.

A. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
B. Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
C. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
D. Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
E. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	coordinate system ⓘ general relativity concept ⓘ spherical coordinate system ⓘ
associatedWith	Schwarzschild radius ⓘ Schwarzschild black hole ⓘ surface form: Schwarzschild solution event horizon of a Schwarzschild black hole ⓘ
assumes	non-rotating central mass ⓘ spherical symmetry ⓘ static spacetime ⓘ
contrastsWith	Kerr coordinates for rotating black holes ⓘ
describes	Schwarzschild black hole ⓘ surface form: Schwarzschild metric exterior region of a static black hole ⓘ spacetime outside a spherically symmetric non-rotating mass ⓘ vacuum solution of Einstein field equations with spherical symmetry ⓘ
domainOfAzimuthalAngle	0 ≤ φ < 2π ⓘ
domainOfPolarAngle	0 ≤ θ ≤ π ⓘ
domainOfRadialCoordinate	0 < r < ∞ ⓘ
domainOfTimeCoordinate	-∞ < t < ∞ ⓘ
hasCoordinate	r ⓘ t ⓘ θ ⓘ φ ⓘ
hasCoordinateSingularityAt	Schwarzschild radius ⓘ
hasCoordinateType	azimuthal angle φ ⓘ polar angle θ ⓘ radial coordinate r ⓘ time coordinate t ⓘ
hasLimitation	breaks down at the event horizon ⓘ not regular across r = 2GM/c^2 ⓘ
hasLineElementForm	ds^2 = -(1-2GM/r)c^2 dt^2 + (1-2GM/r)^{-1} dr^2 + r^2(dθ^2 + sin^2θ dφ^2) ⓘ
hasMetricSignature	(-,+,+,+) ⓘ
hasPhysicalSingularityAt	r = 0 ⓘ
introducedInContextOf	exact solutions of Einstein field equations ⓘ
mathematicallyDefinedOn	Schwarzschild black hole ⓘ surface form: Schwarzschild manifold
namedAfter	Karl Schwarzschild ⓘ
relatedTo	Eddington–Finkelstein coordinates ⓘ Kruskal–Szekeres coordinates ⓘ isotropic coordinates ⓘ
usedFor	calculating gravitational redshift ⓘ calculating light deflection by gravity ⓘ calculating perihelion precession ⓘ studying radial infall into a black hole ⓘ studying test particle orbits ⓘ
usedIn	general relativity ⓘ
usedToDescribe	gravitational field outside a non-rotating black hole ⓘ gravitational field outside a planet ⓘ gravitational field outside a star ⓘ
usesUnits	geometrized units in many treatments ⓘ
validFor	r greater than Schwarzschild radius ⓘ

How these facts were elicited

Referenced by (10)

Full triples — surface form annotated when it differs from this entity's canonical label.

Schwarzschild radius → coordinateSingularityAt → Schwarzschild coordinates ⓘ

Eddington–Finkelstein coordinates → relatedTo → Schwarzschild coordinates ⓘ

Karl Schwarzschild → knownFor → Schwarzschild coordinates ⓘ

Reissner–Nordström metric → hasCoordinateSystem → Schwarzschild coordinates ⓘ

this entity surface form: Schwarzschild-like coordinates

Kruskal–Szekeres coordinates → basedOn → Schwarzschild coordinates ⓘ

Painlevé–Gullstrand coordinates → relatedTo → Schwarzschild coordinates ⓘ

Painlevé–Gullstrand coordinates → hasSpatialCoordinates → Schwarzschild coordinates ⓘ

this entity surface form: Schwarzschild radial coordinate

Schwarzschild → knownFor → Schwarzschild coordinates ⓘ

subject surface form: Karl Schwarzschild

Boyer–Lindquist coordinates → generalizes → Schwarzschild coordinates ⓘ

Karl → hasConceptNamedAfter → Schwarzschild coordinates ⓘ